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A time–frequency representation (TFR) is a view of a signal (taken to be a function of time) represented over both time and frequency. [1] Time–frequency analysis means analysis into the time–frequency domain provided by a TFR. This is achieved by using a formulation often called "Time–Frequency Distribution", abbreviated as TFD.
In the time domain, the usual choice to explore the time response is through the step response to a step input, or the impulse response to a Dirac delta function input. [2] In the frequency domain (for example, looking at the Fourier transform of the step response, or using an input that is a simple sinusoidal function of time) the time ...
The two coincide in fact in NRZ transmission; they do not coincide in a 2B1Q transmission, where one pulse takes the time of two bits. For example, in a serial line with a baud rate of 2.5 Gbit/s, a unit interval is 1/(2.5 Gbit/s) = 0.4 ns/baud.
A time-frequency representation describes the variation of spectral energy distribution over time, much as a musical score describes the variation of musical pitch over time. In audio signal analysis, the spectrogram is the most commonly used time-frequency representation, probably because it is well understood, and immune to so-called "cross ...
A variable measured in discrete time can be plotted as a step function, in which each time period is given a region on the horizontal axis of the same length as every other time period, and the measured variable is plotted as a height that stays constant throughout the region of the time period. In this graphical technique, the graph appears as ...
In mathematics and signal processing, the time domain is a representation of a signal, function, or data set varies with time. [1] It is used for the analysis of mathematical functions, physical signals or time series of economic or environmental data. In the time domain, the independent variable is time, and the dependent variable is the value ...
For example, a TDC might output the time of arrival for each incoming pulse. Some applications wish to measure the time interval between two events rather than some notion of an absolute time, and the digitizer is then used to measure a time interval and convert it into digital (binary) output. In some cases, [1] an interpolating TDC is also ...
In signal processing, time–frequency analysis comprises those techniques that study a signal in both the time and frequency domains simultaneously, using various time–frequency representations. Rather than viewing a 1-dimensional signal (a function, real or complex-valued, whose domain is the real line) and some transform (another function ...